Which layer of skin allows it to move freely over underlying bone and muscle without tearing?

The Hypodermis is the layer of skin that allows it to move freely over the bone and muscle. 

Hypodermis

Explanation:

The hypodermis is also known as the subcutaneous layer which lies beneath the dermis. It is the main storage site of the fat and consists of the adipocytes. It helps to fasten the skin over the surface that lies beneath it and further provides insulation and shock absorbance properties. It further allows the skin to move freely over the underlying surface such as bone and muscle without undergoing any wear and tear.